Algorithms for constructing isolating sets of phase flows and computer-assisted proofs with the use of interval Taylor models

DOI10.1134/S0012266119090088zbMath1429.37049OpenAlexW2980612093WikidataQ113786385 ScholiaQ113786385MaRDI QIDQ2280412

O. I. Ryabkov, N. M. Evstigneev

Publication date: 18 December 2019

Published in: Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0012266119090088

zbMATH Keywords

periodic trajectoriesvalidated numericsconstructive algorithms

Mathematics Subject Classification ID

Periodic orbits of vector fields and flows (37C27) Computational methods for invariant manifolds of dynamical systems (37M21) Symmetries and invariants of dynamical systems (37C79)

Related Items (2)

Analysis and optimization of an adaptive interpolation algorithm for the numerical solution of a system of ordinary differential equations with interval parameters ⋮ Use of shrink wrapping for interval Taylor models in algorithms of computer-assisted proof of the existence of periodic trajectories in systems of ordinary differential equations

Cites Work

• Applicability of the interval Taylor model to the computational proof of existence of periodic trajectories in systems of ordinary differential equations
• Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models
• Topological-numerical approach to the existence of periodic trajectories in ODE's
• Algorithm for the numerical proof of the existence of periodic trajectories in two-dimensional nonautonomous systems of ordinary differential equations
• Validated solutions of initial value problems for parametric ODEs
• Introduction to Interval Analysis
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